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A variety of low-density parity-check (LDPC) ensembles have now been observedto approach capacity with message-passing decoding. However, all of them usesoft (i.e., non-binary) messages and a posteriori probability (APP) decoding oftheir component codes. In this paper, we show that one can approach capacity athigh rates using iterative hard-decision decoding (HDD) of generalized productcodes. Specifically, a class of spatially-coupled GLDPC codes with BCHcomponent codes is considered, and it is observed that, in the high-rateregime, they can approach capacity under the proposed iterative HDD. Thesecodes can be seen as generalized product codes and are closely related tobraided block codes. An iterative HDD algorithm is proposed that enables one toanalyze the performance of these codes via density evolution (DE).

Approaching Capacity at High-Rates with Iterative Hard-Decision Decoding